Opus can preserve folder timestamps when copying files (as long as it is folders created in the process; existing folder timestamps won't be copied over), depending on configuration and also support on the target filesystem (some NAS devices don't support it).
Copying timestamps from one existing directory structure to another isn't something Opus can do out of the box, although a script could be written to do so. I would advise against it, however.
Folder timestamps are very fragile and get changed if any file or folder is created, removed or renamed (and perhaps other operations) below the folder. They can be useful as rough guides to when a folder (but not necessarily the data within it) was last modified, but only as very rough guides.
So before worrying about folder timestamps, I strongly urge you to rethink whatever you have in mind which has led to wanting to preserve them; it is probably not a good idea, even though Opus will let you do it.
A better solution might be to use a column which really reports the newest timestamp of any subfile/folder, without the folder timestamps mattering. There are two scripts which add columns for that:
Custom Column - Newest File (this is the more simple one)
Custom Columns: Newest/Oldest filedate columns w/filtering (more complex one which lets you filter which files are considered)